If seven women and seven men are to be seated | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To ensure that there is a man on either side of every woman,the men and women must alternate around the circular table.First,we arrange the $7$ me

Vedclass · Accepted Answer

$6! 7!$

Vedclass · Answer

(A) To ensure that there is a man on either side of every woman,the men and women must alternate around the circular table.First,we arrange the $7$ men around the circular table. The number of ways to arrange $n$ items in a circle is $(n-1)!$. Thus,$7$ men can be seated in $(7-1)! = 6!$ ways.Once the men are seated,there are $7$ distinct gaps created between them.Since every woman must have a man on either side,we must place the $7$ women into these $7$ gaps.The number of ways to arrange $7$ women in these $7$ gaps is $7!$.Therefore,the total number of seating arrangements is $6! 	imes 7!$.

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

Similar Questions

How many numbers lying between $1000$ and $10000$ can be formed by using the digits $1, 3, 5, 6, 7, 8, 9$ if no digits are repeated?

In how many different ways can the letters of the word '$KURUKSHETRA$' be arranged?

Find the number of all even $2$-digit numbers that do not have $0$ at the unit's place.

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

How many numbers can be formed with the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy the odd places?

Vedclass Test Series

Exam Paper Generator

Online Exam Module